The formula in terms of x and y for dy/dx is y/ -2x
The value of dy/dx at the point (1,1) is -0.5
The question is incomplete, the full question is given below:
200 cars can produced when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 45 x^1/3 y^2/3= 200
a. Find a formula in terms of x and y for dy/dx
b. Find the value of dy/dx at the point (1,1). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for dy/dx
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=d/dx(45 x^1/3 y^2/3) =d/dx( 200)
=> 45 *(1/3) x^-2/3 y^2/3 + 45 x^1/3 2/3 y^ -1/3 dy/dx=0
=> x^-2/3y^2/3+ 2 x^1/3 y^-1/3 dy/dx=0
=> y/x= -2dy/dx
=> log y = -2 log x +log c
=> y= x^ -2 +c
putting x=y=1
c=0
then y= 1/x^2
b) y/x= -2dy/dx
put x=y=1 we get
-1/2 = dy/dx
dy/dx =-0.5
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30 POINTS! What is the domain and range of g(x) = |x + 4|
Answer:
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
1. You launch a toy rocket from a height of 5 feet. The height h, in feet of the rocket t seconds after taking off is given by the formula h = -3t2 + 14t + 5.
In case whereby You launch a toy rocket from a height of 5 feet with the height h, in feet of the rocket t seconds after taking off is given by the formula h = -3t2 + 14t + 5, then the value of t will be 4.67 secs.
How can the values of t be calculated?
The giving equation is h = -3t2 + 14t + 5
where the height h is been given as 5 feet, then we can substitute the value of the height they the expression can be simplified as
5 = -3t^2 + 14t + 5
Then this equation can be re arranged as :
-3t^2 + 14t + 5 - 5=0
This can as well be expressed as
-3t^2 + 14t = 0
t(-3t + 14)= 0
Then t= 0 and -3t + 14=0
t=14/3 = 4.67 secs
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How do you write 8.61 × 10–1 in standard form?
The expression 8.61 x 10-1 in standard form is 0.861
How to rewrite the expression?The expression is given as
8.61 x 10-1
Rewrite the equation properly as follows
So, we have the following expression
8.61 x 10^-1
Express 10^-1 as 1/10
So, we have the following expression
8.61 x 1/10
Evaluate the products
So, we have the following expression
8.61/10
Evaluate the quotient
So, we have the following expression
0.861
Hence, the expression is 0.861
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What is the rate of change of the following equation? y=5/3x - 3
Answer:
5/3 is the slope. slope is the same thing as rate of change
Step-by-step explanation:
Three cups of oatmeal are used to make 24 oatmeal cookies. How many cups of oatmeal are needed to make 36 oatmeal cookies?
someone please help me???
Simplify the expression.[(-5)1]3
The simplified expression is -125.
The expression given to us is [(-5)^1]³.In contrast to algebraic expressions, which include variables, numbers, and mathematical operators, arithmetic expressions simply contain numbers and mathematical operators.There are several laws of indices, often known as indices rules, including those governing division, multiplication, power of 0, brackets, negative powers, and fractional powers.We need to apply the laws of indices given below :(a^m)^n = a^(mn)Applying the above rule to our given expression.[(-5)^1]³ = (-5)^(1*3)The expression is simplified further.[(-5)^1]³ = (-5)³We know that a negative number raised to an odd power is always negative.[(-5)^1]³ = -125.Thus, the final simplified expression is -125.To learn more about indices, visit :
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Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
(x, y) - (x.-y)
(x,y) - (y.x)
(x,y) - (-x.-y)
(x,y) - (-y.-x)
Option C, (x, y) - (-x, -y) is the rule which describes the transformation.
A rotation in geometry is a change of a shape that involves turning it by a given number of degrees around a certain point known as the center of rotation and is denoted as R(0,x), wherein x is an angle of rotation around a center point O.
Assume triangle ABC's subsequence to be (x, y) and the angle of rotation for rotating triangle ABC to A'B'C' to be 180° or -180° about the center of rotation (0,0).
That is under R(0,0),180°.
The image formed is (-x,-y).
The resulting picture will contain a triangle ABC in the first quadrant of the graph and a triangle A'B'C inside the third quadrant with the center of rotations (0,0).
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a couple plans to have three children. there are eight possible arrangements of girls and boys. for example, ggb means the first two children are girls and the third child is a boy. all eight arrangements are (approximately) equally likely.
The sample space of the three children that the couple will have will be:
S = (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG)
How to illustrate the information?From the information given, the couple plans to have three children. there are eight possible arrangements of girls and boys.
Therefore, the sample space of the three children will be:
N(S) = 2³
= 2 × 2 × 2
= 8
The eight arrangements are illustrated above.
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solve the absolute value inequality and express the solution in interval and algebraic notation
Answer:
[-10, - 2]
Step-by-step explanation:
1
Solve the inequality: ly+ 61 - 4 <0
-10 ≤ and ≤-2
2 Express solution set in interval notation:
[-10, -2]
An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide.
Type the answers to the questions below in the boxes.
1. What scale is being used for the image?
inch to
inches
2. How tall is the actual book?
inches
The height will be 18 inches and the scale is 1 inch = 6 inches.
1.5 inches is the width of a book picture shown on a website.
And the book's length, as displayed on the website, is 3 inches
The book's real width is 9 inches.
The book image's size is
6 inches to one inch
The book is actually three and six pages long.
The size of the real book is 18 inches long and 9 inches broad.
Hence the scale is 1 inch is equal to 6 inches and height is 18 inches.
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Find the equation of the line that is perpendicular to the line y =5x + 6 and passes through the point (-3,3). Write the equation in point slope form.
The point-slope form of equation of the line perpendicular to the line y = 5x + 6 nd passing through (-3,3) is x + 5y = 12.
If two lines are perpendicular to each other, then the product of slopes of these two lines is equal to -1.
The provided line is y = 5x + 6,
The slope M₁ of the line is equal to the coefficient of x,
M₁ = 5
Let the slope of the perpendicular line is M₂,
So, we can write,
M₁M₂ = -1
M₂ = -1/5.
Now, we can use the point slope form of the equation of line, according to which is if line passes through (a,b) and have slope m then the equation of the line will be,
(y-a) = m(x-a)
This form of line is called Point-slope form of line.
Then, the equation of the line with slope -1/5 and passing through (-3,3) will be,
(y-3) = -1/5(x+3)
-5y+15 = x+3
x + 5y = 12
The above equation is the required equation of line in point slope form.
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whait is the formula of mean deviation
The formula of mean deviation = [Σ |X – µ|]/N
What is mean deviation?
Mean deviation defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set.
The formula of mean deviation is [Σ |X – µ|]/N
Here,
Σ represents the addition of values
X represents each value in the data set
µ represents the mean of the data set
N represents the number of data values.
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1. Compare two spheres. The first has a diameter of 4 inches.
The second sphere has a diameter of 428 inches.
Determine the ratio of the volume of the large sphere to the volume
of the small sphere.
Ratio =
Answer:
1,225,043
Step-by-step explanation:
You want the ratio of volumes of spheres 428 inches and 4 inches in diameter.
VolumeThe volume of a sphere in terms of its diameter is ...
V = (π/6)d³
The ratio of the volumes of the larger to smaller sphere is ...
[tex]\dfrac{V_{large}}{V_{small}}=\dfrac{\pi/6\cdot428^3}{\pi/6\cdot4^3}=\left(\dfrac{428}{4}\right)^3=107^3=\boxed{1,\!225,\!043}[/tex]
The ratio of volumes is 1,225,043.
The ratio of the volume of the large sphere to the volume of the small sphere is 1225043:1
The following is the formula for finding the volume of a sphere:
V = [tex]\frac{4}{3} \pi r^3[/tex]
Now, the normal assumption is that we must use the formula to calculate the volume of both spheres in order to compare. However, observe that in comparing the volume of two different spheres, the only difference between them is the radius, thus we can compare the two spheres directly in this way:
[tex]\frac{(radius of sphere B)^3 }{(radius of sphere A)^3}[/tex]
So,
[tex](\frac{428}{4})^3[/tex]
[tex]107^3[/tex]:1
12,25,043:1.
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write an equation which relates the figure number x to the number of tiles y
Write an equation which relates the figure number x to the number of tiles y
x= increase a row of 4 per image
y = 1 + 4*x
Figures
1
y = 1 + 4*(1) = 5
2
y = 1 + 4*(2) = 11
3
y = 1 + 4*(3) = 13
__________________
Answer
The equation which relates the figure number x to the number of tiles y is
y = 1 + 4x
_
Can you see the updates?
Do you have any questions regarding the solution?
when a study uses – , each member of a population has an equal chance of being selected. – occurs when researchers randomly sample subsets of the population and then use all individuals within the subsets. – is often used to select participants to represent, in an unbiased way, subsets of the population that are not large enough to be accurately measured. all three of these techniques are – sampling techniques.
When a study uses random sampling, each member of a population has an equal chance of being selected.
Cluster sampling occurs when researchers randomly sample subsets of the population and then use all individuals within the subsets.
Oversampling is often used to select participants to represent, in an unbiased way, subsets of the population that are not large enough to be accurately measured.
All all three of these techniques are representative sampling techniques.
What is sampling?It should be noted that sampling simply means the selection of subjects from the entire population.
In a random sampling, everyone has equal opportunity of being picked.
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Jade has four slices of chocolate cake.
She gives a slice to Josh, Malaysia, and Jacob.
What fraction of the cake did Jade give away?
Jade give away 3/4 fraction of the cake.
Solve negative a minus four sevenths equals two thirds for a.
a equals negative 26 over 21
a equals 26 over 21
a equals negative 2 over 21
a equals 2 over 21
The solution for the linear equation is a = -26/21, so the correct option is the first one counting from the top.
How to solve the linear equation?Here we have a mathematical statement that can be written as the following linear equation:
-a - 4/7= 2/3
To solve this for a, we just need to isolate a in one of the sides of the equation, so let's do taht.
-a - 4/7 = 2/3
a = -4/7 - 2/3
Now we need a common denominator in the right side, i will use 21.
a = -12/21 - 14/21 = -26/21
So the correct option is the first one.
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Mark has a container in the shape of a cube. He uses 64 cubes with sides lengths of 1 inch to completely fill the container.
What is the edge length of the container?
Hint: The volume of the container is 64 cubic inches.
If Mark has a container in the shape of a cube and he uses 64 cubes with sides length of 1 inch to completely fill the container, then the edge length of the container is 4 inches
The shape of the container is cube
He uses 64 cubes with side length of 1 inch to completely fill the container
The volume of cube with side length of 1 inches = [tex]a^{3}[/tex]
Where a is the side length of the cube
= [tex]1^{3}[/tex]
= 1 cubic inches
The volume of 64 cubes = 64×1
= 64 cubic inches
The volume of the container in cub shape = The volume of the 64 cubes with side length of 1 inches
[tex]a^{3}[/tex] = 64
a = 4 inches
Hence, if Mark has a container in the shape of a cube and he uses 64 cubes with sides length of 1 inch to completely fill the container, then the edge length of the container is 4 inches
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I wills end you a picture
The rate of change is represented by the slope of each club.
For Club A is 12.
For Club B we calculate using the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{42-21}{2-1} \\ m=\frac{21}{1}=21 \end{gathered}[/tex]The value is 21.
For Club C we apply the same formula and use the poins shown in the graphic
[tex]\begin{gathered} m=\frac{70-40}{3-1} \\ m=\frac{30}{2} \\ m=15 \end{gathered}[/tex]For club D the slope is the value that is paid each month
which in this case is $20
According to this the greatest rate of chande is for Health Club B
Alice was given 15.5 divided by 0.25 to divide. Alice says she knows the way that she can find the quotient without even dividing. Is Alice correct?
Answer:
i'm not sure i looked it up but from it says you you can find the quotient by using the opposite of division which is multiplying again I'm not sure i might be wrong but please let me know if its right
Step-by-step explanation:
NEED HELP IMMEDIATELY!!!
Answer:
1. m∠P + m∠Q + m∠R = 180°
2. x = 10
Step-by-step explanation:
By the triangle sum theorem, the sum of the angles in a triangle is 180°. Therefore, using the given sum theorem, m∠P + m∠Q + m∠R = 180°. Using the substitution property, (5x)° + (5x)° + (8x)° = 180°. Simplifying the equation gets 18x = 180°. Finally, using the division property of equality, x = 10.
I hope this helps!
9 girls and 3 boys write left-handed what is the percent
Answer:
You need more context.
Step-by-step explanation:
What percentage are we solving for?
24. a. The 2004 Toyota Corolla is advertised by Toyota as getting 32 miles to the gallon while driving around town. We will assume that Toyota is rounding this number to the units place. The fuel tank holds 13.2 gallons. If the tank is full, how many miles could drive before running out of gas? Round according the guidelines.
b. AAA ran tests on fuel efficiency and found the 2004 Toyota Corolla actually got 28.9 miles per gallon driving around town. Using AAA's estimate, how long could you drive before running out of gas? Round according the guidelines.
c. How many miles less does the AAA estimate predict you can get on a single tank of gas? Round according the guidelines.
a) If the tank is full, using mathematical operations based on the 2004 Toyota Corolla, you will run 422.4 miles before running out of gas, according to Toyota's advert.
b) Using AAA's estimate, one could drive 381.4 miles before running out of gas.
c) Based on the AAA estimate, on a single tank of gas, you can predict that you will get 40.9 miles less.
What are mathematical operations?The mathematical operations include subtraction, addition, division, and multiplication.
For our purpose, we have used the mathematical operations of multiplication and subtraction to determine the above values.
Claimed mileage per gallon, according to the Toyota advert = 32 miles
The number of gallons of gas in Toyota Corolla's full tank = 13.2 gallons.
AA fuel efficiency on 2004 Toyota Corolla = 28.9 mpg
a) Miles to run before running out of gas (Toyota advert) = 422.4 (32 x 13.2) miles
b) Miles to run before running out of gas (AAA rating) = 381.48 (28.9 x 13.2) miles
c) The difference in miles between (a) and (b) above = 40.92 (422.4 - 381.48) miles
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The graph of the equation y = 4x + 2, what is the y when x = 1?
Answer: 6
Step-by-step explanation:
[tex]y=4(1)+2=6[/tex]
the populations of towns a, b, and c vary exponentially with respect to time. the population of town a increases by 26% every 11 years. what is the annual percent change in the population of town a? % the population of town b decreases by 39% every 13 years. what is the annual percent change in the population of town b? % the population of town c triples every 5 years. what is the annual percent change in the population of town c?
a. 11 year growth factor = 1 + (26/100) = 1.26
1-year growth factor = (1.26)^1/11 = 1.0210
Therefore,
1-year growth percent = 1.0210 - 1 = 0.0210 %
Answer: 2.10
b. 13-year decay factor = 1 - (39/100) = 0.61
1-year decay factor = (0.61)1/13 = 0.9631
Therefore,
13-year decay factor = 1 - 0.9631 = 0.03686 = 3.68%
Answer: 3.68
c. 5-year growth factor = 3
1-year growth factor = (3) ^1/5 = 1.245
Therefore,
1-year growth factor = 1.2457 - 1 = 0.2457 = 2.45%
Answer:2.45
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May you guys/girls please help me I have to submit this befoer mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Answer down below!
Step-by-step explanation:
Lets start off by finding a point we can start off at!
Since (2,0) lands perfectly on the number line, we can use that one!
From there, use the rise/run method to find your slope
We go up 2 and over -2
Thus our fraction is -2/2 BUT WE AREN'T DONE!
We can simplify this to be -1/1 or -1
Thus, our slope is -1
It's negative one, starting from the y intercept you're going down one right one and so on.
What are the next three terms
125, -25, 5, ...
Answer:
25, 125, 3125, 78125, 1953125
Answer:
-1 ; 1/5 ; -1/25
Step-by-step explanation:
125 : (-5) = -25
-25 : (-5) = 5
5 : (-5) = -1
-1 : (-5) = 1/5
1/5 : (-5) = -1/25
Jake spent a total of $40 dollars on the items below 4 movie tickets for $6 each 2 bags of popcorn for $7 4 drinks for $2.25 each what percent of the $40 did jake spend on movie tickets?
Answer: Jake spent 62.5% of the money on movie tickets.
Step-by-step explanation: He spent 6 x 4 = $24 on movie tickets.
He spent 7 x 2.25 = 15.75 on drinks
However, it is asking for the amount of money he spent on MOVIE TICKETS. So then it would be 25/40 or 5/8.
A concession stand sells drinks and hotdogs. The number of drinks sold is 5 more than 4 times the number of hotdogs sold. The stand sold 500 items. How many hotdogs were sold?
Pleas help
Two or more expressions with an equal sign is called as Equation. We solve the problem by forming equations, After solving equations we came to know that 123 hotdogs were sold in the concession stand.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Given that,
A concession stand sells drinks and hotdogs.
The number of drinks sold is 5 more than 4 times the number of hotdogs sold.
The stand sold 500 items.
Let the number of hotdogs=x
The number of drinks sold is 5 more than 4 times the number of hotdogs sold.
The number of drinks=5+4x
stand sold 500 items.
Let us formulate a equation by given data
5+4x=500
Let us separate the variable x on one side.
Subtract 5 on both sides
5+4x-5=500-5
4x=500-5
4x=495
Divide both sides by 4
x=123.25
Hence 123 hotdogs were sold in the concession stand.
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Draw a coordinate plane on your paper. Then
plot the points on your coordinate plane.
A(3, 1) B(2, 4) C(4, 1) D(1, 5)
Answer:
yw:) have a good day :)